\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13 - 2D Segment Delaunay Graphs
CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2< CK, CM, EK, EM, FK, FM > Struct Template Reference

#include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>


The class Segment_Delaunay_graph_filtered_traits_without_intersections_2 provides a model for the SegmentDelaunayGraphTraits_2 concept.

The class Segment_Delaunay_graph_filtered_traits_without_intersections_2 uses the filtering technique [1] to achieve traits for the Segment_Delaunay_graph_2<Gt,DS> class with efficient and exact predicates given an exact kernel EK and a filtering kernel FK. The geometric constructions associated provided by this class are equivalent to those provided by the traits class Segment_Delaunay_graph_traits_without_intersections_2<CK,CM>, which means that they may be inexact, depending on the choice of the CK kernel.

This class has six template parameters.

Template Parameters
CKis the construction kernel and it is the kernel that will be used for constructions.
CMmust be Field_with_sqrt_tag or Field_tag
FKis the filtering kernel; this kernel will be used for performing the arithmetic filtering for the predicates involved in the computation of the segment Delaunay graph.
FMmust be Field_with_sqrt_tag or Field_tag
EKis the exact kernel; this kernel will be used for computing the predicates if the filtering kernel fails to produce an answer.
EMmust be Field_with_sqrt_tag or Field_tag

The first, third and fifth template parameters must be a models of the Kernel concept. The second, fourth and sixth template parameters correspond to how predicates are evaluated. There are two predefined possible values for these parameters, namely Field_with_sqrt_tag and Euclidean_ring_tag. The first one must be used when the number type used in the representation supports the exact evaluation of signs of expressions involving all four basic operations and square roots, whereas the second requires the exact evaluation of signs of ring-type expressions, i.e., expressions involving only additions, subtractions and multiplications. Finally, in order to get exact constructions CM must be set to Field_with_sqrt_tag and the number type in CK must support operations involing divisions and square roots (as well as the other three basic operations of course). The way the predicates are evaluated is discussed in [2] and [4] (the geometric filtering part).

The default values for the template parameters are as follows:

Is Model Of:





See also
Segment_Delaunay_graph_2/sdg-fast-sp-polygon.cpp, and Segment_Delaunay_graph_2/sdg-fast-sp.cpp.


In addition to the types required by the SegmentDelaunayGraphTraits_2 concept the class Segment_Delaunay_graph_filtered_traits_without_intersections_2 defines the following types:

typedef CGAL::Tag_false Intersections_tag
typedef CK Kernel
typedef CK Construction_kernel
typedef FK Filtering_kernel
typedef EK Exact_kernel
typedef CM Method_tag
typedef CM Construction_traits_method_tag
typedef FM Filtering_traits_method_tag
typedef EM Exact_traits_method_tag
typedef unspecified_type Construction_traits
 A type for the segment Delaunay graph traits, where the kernel is CK.
typedef unspecified_type Filtering_traits
 A type for the segment Delaunay graph traits, where the kernel is FK.
typedef unspecified_type Exact_traits
 A type for the segment Delaunay graph traits, where the kernel is EK.